G asserts its own unprovability in F

[Skepdick]

The same nitwit that honestly believes that
FALSE <proves> Donald Trump is the Christ

also believes that expressions of language with currently unknown truth values
(conjectures in math) are IMPOSSIBLE TO RESOLVE TO TRUE OR FALSE.

Olcott, you are [Redacted].

Please provide the truth-value for P=NP.
Please provide the truth-value for P=NP is not provable.
Please provide the truth-value for P=NP is provable.


[Edited by iMod]

[Agent Smith]

I'm still in the dark about Gödel numbering; I hear it's critical to his proofs of incompleteness.

Anyway, PeteOlcott seems to have homed in on a flaw in Gödel's argument and it kinda sorta aligns with my own suspicions in re Gödel's work. The penny ultimately ... hasta drop, oui?

I can somewhat sense the urgency of the matter i.e. there's at least one very good reason why Gödel should keep us awake at night, but that's a topic for another discussion. Oui?

[PeteOlcott]

I'm still in the dark about Gödel numbering; I hear it's critical to his proofs of incompleteness.

Anyway, PeteOlcott seems to have homed in on a flaw in Gödel's argument and it kinda sorta aligns with my own suspicions in re Gödel's work. The penny ultimately ... hasta drop, oui?

I can somewhat sense the urgency of the matter i.e. there's at least one very good reason why Gödel should keep us awake at night, but that's a topic for another discussion. Oui?

The key urgency of the matter is to divide the opposing ideas:
(a) Putin invaded Ukraine as a land grab to bring back that Russian empire.
(b) Putin invaded Ukraine to legitimately prevent hostile powers from getting too close to its borders
in a way similar to the Cuban Missile Crisis.

Whether or not there was substantial voter fraud that changed the outcome of the
2020 presidential election.

Whether or not climate changed is actually caused by humans and what are the reasonably
plausible range of best case to worst case scenarios of simply ignoring it.

My ultimate goal is to make True(L,x) computable.

Here is a brief overview of my greatest impediment to that goal:
The idea of the proof: If there were such a formula of the language of F, an easy application
of the Diagonalization Lemma to its negation would result in the paradoxical sentence
L (for “Liar”; see the Liar paradox)), such that: F ⊢ ¬Tr(┌L┐) ↔ L,

which, together with the T-equivalences, which were assumed to be derivable, would quickly
give an explicit contradiction, thus contradicting the assumption that F is consistent.
https://plato.stanford.edu/entries/goed ... rTheUndTru

In other words Tarski could not prove that the self-contradictory Liar Paradox is true
so he concluded that True(F,x) cannot be correctly defined in F.

Here is how Tarski "proved" that the Liar Paradox is true in his metatheory:
This sentence is not true: "This sentence is not true"

Here is his original proof: https://liarparadox.org/Tarski_275_276.pdf

The Liar Paradox is very obviously not a truth bearer
https://plato.stanford.edu/entries/truthmakers/

My unique contribution to this field is that there are a set of finite strings of language L
that are stipulated to have the semantic property of Boolean True these are the truth makers of L.

For formal languages Haskell Curry called these the
elementary theorems of::t
https://www.liarparadox.org/Haskell_Curry_45.pdf

I extend this notion to natural languages such that {cats are animals} is stipulated
to be true in the model of the current world of all possible worlds.
Thus True(L, x) merely means that x is derived from the axioms of formal or natural language L.

What I mean by derived requires a separate discussion.
It is essentially a formal syntactic proof from the axioms of L to x using only semantically
truth preserving operations. At a minimum this requires relevance logic.
https://plato.stanford.edu/entries/logic-relevance/

[Agent Smith]

I'm still in the dark about Gödel numbering; I hear it's critical to his proofs of incompleteness.

Anyway, PeteOlcott seems to have homed in on a flaw in Gödel's argument and it kinda sorta aligns with my own suspicions in re Gödel's work. The penny ultimately ... hasta drop, oui?

I can somewhat sense the urgency of the matter i.e. there's at least one very good reason why Gödel should keep us awake at night, but that's a topic for another discussion. Oui?

The key urgency of the matter is to divide the opposing ideas:
(a) Putin invaded Ukraine as a land grab to bring back that Russian empire.
(b) Putin invaded Ukraine to legitimately prevent hostile powers from getting too close to its borders
in a way similar to the Cuban Missile Crisis.

Whether or not there was substantial voter fraud that changed the outcome of the
2020 presidential election.

Whether or not climate changed is actually caused by humans and what are the reasonably
plausible range of best case to worst case scenarios of simply ignoring it.

My ultimate goal is to make True(L,x) computable.

Here is a brief overview of my greatest impediment to that goal:
The idea of the proof: If there were such a formula of the language of F, an easy application
of the Diagonalization Lemma to its negation would result in the paradoxical sentence
L (for “Liar”; see the Liar paradox)), such that: F ⊢ ¬Tr(┌L┐) ↔ L,

which, together with the T-equivalences, which were assumed to be derivable, would quickly
give an explicit contradiction, thus contradicting the assumption that F is consistent.
https://plato.stanford.edu/entries/goed ... rTheUndTru

In other words Tarski could not prove that the self-contradictory Liar Paradox is true
so he concluded that True(F,x) cannot be correctly defined in F.

Here is how Tarski "proved" that the Liar Paradox is true in his metatheory:
This sentence is not true: "This sentence is not true"

Here is his original proof: https://liarparadox.org/Tarski_275_276.pdf

The Liar Paradox is very obviously not a truth bearer
https://plato.stanford.edu/entries/truthmakers/

My unique contribution to this field is that there are a set of finite strings of language L
that are stipulated to have the semantic property of Boolean True these are the truth makers of L.

For formal languages Haskell Curry called these the
elementary theorems of::t
https://www.liarparadox.org/Haskell_Curry_45.pdf

I extend this notion to natural languages such that {cats are animals} is stipulated
to be true in the model of the current world of all possible worlds.
Thus True(L, x) merely means that x is derived from the axioms of formal or natural language L.

What I mean by derived requires a separate discussion.
It is essentially a formal syntactic proof from the axioms of L to x using only semantically
truth preserving operations. At a minimum this requires relevance logic.
https://plato.stanford.edu/entries/logic-relevance/

That's a lot to process bruh!

There's a Roger Penrose supershort video on Gödel's theorems. Watch it here https://youtu.be/w11mI67R95I and get back to me ... if you wish.

Addendum: Does Gödel get lost in wordplay?

[PeteOlcott]

That's a lot to process bruh!

There's a Roger Penrose supershort video on Gödel's theorems. Watch it here https://youtu.be/w11mI67R95I and get back to me ... if you wish.

Addendum: Does Gödel get lost in wordplay?

Those were the technical details meant for technical readers. I just
watched the video. It boils down to what I have been saying many
times in this forum (no one else every boiled it down correctly)

When G asserts that it cannot be proven in the formal system
named F a proof of G in F would prove that itself does not exist.

On the other hand metamathematics can prove that G cannot
be proved in F because this proof is not self-contradictory in
metamathematics.

This sums things up the same way as the video yet unlike anyone
ever before it sums up the reason why G cannot be proved in F.
G cannot be proved in F because G is semantically unsound in F.

The above is the correct essence of Gödel's 1931 theorem.

[Agent Smith]

That's a lot to process bruh!

There's a Roger Penrose supershort video on Gödel's theorems. Watch it here https://youtu.be/w11mI67R95I and get back to me ... if you wish.

Addendum: Does Gödel get lost in wordplay?

Those were the technical details meant for technical readers. I just
watched the video. It boils down to what I have been saying many
times in this forum (no one else every boiled it down correctly)

When G asserts that it cannot be proven in the formal system
named F a proof of G in F would prove that itself does not exist.

On the other hand metamathematics can prove that G cannot
be proved in F because this proof is not self-contradictory in
metamathematics.

This sums things up the same way as the video yet unlike anyone
ever before it sums up the reason why G cannot be proved in F.
G cannot be proved in F because G is semantically unsound in F.

The above is the correct essence of Gödel's 1931 theorem.

Danke! Discussing Gödel with ya has been an amazing learning experience for me. I now possess a clearer picture of the problem. Again, gracias.

My suggestion would be to pay close attention to the formal (symbolic) statement of Gödel's theorems (I quoted it once).

[Agent Smith]

TIMTOWDI?!

Simple ...

A cat!

We need ta get us some skin!

[PeteOlcott]

That's a lot to process bruh!

There's a Roger Penrose supershort video on Gödel's theorems. Watch it here https://youtu.be/w11mI67R95I and get back to me ... if you wish.

Addendum: Does Gödel get lost in wordplay?

Those were the technical details meant for technical readers. I just
watched the video. It boils down to what I have been saying many
times in this forum (no one else every boiled it down correctly)

When G asserts that it cannot be proven in the formal system
named F a proof of G in F would prove that itself does not exist.

On the other hand metamathematics can prove that G cannot
be proved in F because this proof is not self-contradictory in
metamathematics.

This sums things up the same way as the video yet unlike anyone
ever before it sums up the reason why G cannot be proved in F.
G cannot be proved in F because G is semantically unsound in F.

The above is the correct essence of Gödel's 1931 theorem.

Danke! Discussing Gödel with ya has been an amazing learning experience for me. I now possess a clearer picture of the problem. Again, gracias.

My suggestion would be to pay close attention to the formal (symbolic) statement of Gödel's theorems (I quoted it once).

Gödel's G is the yellow highlight at the top of the page:
https://www.liarparadox.org/G%C3%B6del_ ... (1931).pdf
It needs many formulas to defines its elements.

[Agent Smith]

Those were the technical details meant for technical readers. I just
watched the video. It boils down to what I have been saying many
times in this forum (no one else every boiled it down correctly)

When G asserts that it cannot be proven in the formal system
named F a proof of G in F would prove that itself does not exist.

On the other hand metamathematics can prove that G cannot
be proved in F because this proof is not self-contradictory in
metamathematics.

This sums things up the same way as the video yet unlike anyone
ever before it sums up the reason why G cannot be proved in F.
G cannot be proved in F because G is semantically unsound in F.

The above is the correct essence of Gödel's 1931 theorem.

Danke! Discussing Gödel with ya has been an amazing learning experience for me. I now possess a clearer picture of the problem. Again, gracias.

My suggestion would be to pay close attention to the formal (symbolic) statement of Gödel's theorems (I quoted it once).

Gödel's G is the yellow highlight at the top of the page:
https://www.liarparadox.org/G%C3%B6del_ ... (1931).pdf
It needs many formulas to defines its elements.

I havta bow out of the discussion now. Too technical for my taste.

I'll leave you with a few thoughts of mine:

1. Look for (logical) equivalences [it appears that you're fully aware of them, one in particular interests me the most]

2. The essence of logic, by extension math, is to study classes of objects.

3. Carefully study ... each step in ... Gödel's argument.

Mind you, these points don't necessarily imply Gödel is wrong. They're simply aspects of Gödel's argument I find are weak/suspect/dubious.

Have a good day

[PeteOlcott]

I havta bow out of the discussion now. Too technical for my taste.

I'll leave you with a few thoughts of mine:

1. Look for (logical) equivalences [it appears that you're fully aware of them, one in particular interests me the most]

2. The essence of logic, by extension math, is to study classes of objects.

3. Carefully study ... each step in ... Gödel's argument.

Mind you, these points don't necessarily imply Gödel is wrong. They're simply aspects of Gödel's argument I find are weak/suspect/dubious.

Have a good day

The heart of the matter does not involve any math at all.
https://plato.stanford.edu/entries/self ... #WhyParMat
The part that involves math is extraneous to the heart of the matter.

Let continue to discuss the actual heart of the matter.

[Agent Smith]

I havta bow out of the discussion now. Too technical for my taste.

I'll leave you with a few thoughts of mine:

1. Look for (logical) equivalences [it appears that you're fully aware of them, one in particular interests me the most]

2. The essence of logic, by extension math, is to study classes of objects.

3. Carefully study ... each step in ... Gödel's argument.

Mind you, these points don't necessarily imply Gödel is wrong. They're simply aspects of Gödel's argument I find are weak/suspect/dubious.

Have a good day

The heart of the matter does not involve any math at all.
https://plato.stanford.edu/entries/self ... #WhyParMat
The part that involves math is extraneous to the heart of the matter.

Let continue to discuss the actual heart of the matter.

I've already submitted a few points on Gödel for you to process. What became of that?

[PeteOlcott]

The heart of the matter does not involve any math at all.
https://plato.stanford.edu/entries/self ... #WhyParMat
The part that involves math is extraneous to the heart of the matter.

Let continue to discuss the actual heart of the matter.

I've already submitted a few points on Gödel for you to process. What became of that?

The issue with Gödel is outside of his actual proof and actually lies with the notion of
epistemological entailment. His proof relies on epistemological antinomies, and the
linked article

The significance of a paradox is its indication of a flaw or deficiency in our understanding of the central concepts involved in it. In case of the semantic paradoxes, it seems that it is our understanding of fundamental semantic concepts such as truth (in the liar paradox and Grelling’s paradox) and definability (in Berry’s and Richard’s paradoxes) that are deficient.

Since both Gödel and Tarski rely on epistemological antinomies [AKA paradoxes] and the existence
of paradoxes indicates that our understanding is incorrect then Tarski and Gödel are anchored
in misunderstanding.

[Agent Smith]

The heart of the matter does not involve any math at all.
https://plato.stanford.edu/entries/self ... #WhyParMat
The part that involves math is extraneous to the heart of the matter.

Let continue to discuss the actual heart of the matter.

I've already submitted a few points on Gödel for you to process. What became of that?

The issue with Gödel is outside of his actual proof and actually lies with the notion of
epistemological entailment. His proof relies on epistemological antinomies, and the
linked article

The significance of a paradox is its indication of a flaw or deficiency in our understanding of the central concepts involved in it. In case of the semantic paradoxes, it seems that it is our understanding of fundamental semantic concepts such as truth (in the liar paradox and Grelling’s paradox) and definability (in Berry’s and Richard’s paradoxes) that are deficient.

Since both Gödel and Tarski rely on epistemological antinomies [AKA paradoxes] and the existence
of paradoxes indicates that our understanding is incorrect then Tarski and Gödel are anchored
in misunderstanding.

The follow-up question be obvious then, eh?

[PeteOlcott]

The issue with Gödel is outside of his actual proof and actually lies with the notion of
epistemological entailment. His proof relies on epistemological antinomies, and the
linked article

The significance of a paradox is its indication of a flaw or deficiency in our understanding of the central concepts involved in it. In case of the semantic paradoxes, it seems that it is our understanding of fundamental semantic concepts such as truth (in the liar paradox and Grelling’s paradox) and definability (in Berry’s and Richard’s paradoxes) that are deficient.

Since both Gödel and Tarski rely on epistemological antinomies [AKA paradoxes] and the existence
of paradoxes indicates that our understanding is incorrect then Tarski and Gödel are anchored
in misunderstanding.

The follow-up question be obvious then, eh?

I don't know what you mean.
I am looking into epistemological entailment also called epistemological closure.

It only took me a few minutes to address: The Gettier problem
Knowledge is not merely a justified true belief

Knowledge is a fully justified true belief such the the justification
conclusively proves that the belief is true.

[Agent Smith]

The issue with Gödel is outside of his actual proof and actually lies with the notion of
epistemological entailment. His proof relies on epistemological antinomies, and the
linked article



Since both Gödel and Tarski rely on epistemological antinomies [AKA paradoxes] and the existence
of paradoxes indicates that our understanding is incorrect then Tarski and Gödel are anchored
in misunderstanding.

The follow-up question be obvious then, eh?

I don't know what you mean.
I am looking into epistemological entailment also called epistemological closure.

It only took me a few minutes to address: The Gettier problem
Knowledge is not merely a justified true belief

Knowledge is a fully justified true belief such the the justification
conclusively proves that the belief is true.

We're reading the same book then! You're a good person PeteOlcott. I'm on Khan Academy and I own about 20 Tenacity badges. You earn them when you fall and get up ... many, many times ... figuratively speaking.

Follow the links ... Gödel's proof is a nightmare of them.